what about using a e natural logarithm as M on small portions of data giving the X value, i dont see how it would matter what M= so long as it gives x(X being a portion of the string) then taking the next 5 values and using an e logarithm and so on. Would this not end in the total value of X ?the best compression we can achieve for any string x is to encode it as the shortest program M in some language L that outputs x.

I have been studying Matt :P love reading your book

ps my friend was telling me that e natural logarithm's where being used before computers where invented "P

Never mind i just read this article http://www.faqs.org/faqs/compression...section-8.html on random data compression and realize it cant be done

And there i was thinking of a random brute force algorithm that worked by splitting up the x string into 6 digit decimal chunks and randomly discovering the right formula, then moving on to the next 6 digits. I still find it hard to believe its impossible after reading Harking's theory on possibility. But i must admit it would be hard to get 16 pigeons into 15 holes.